Related papers: The Shape and Stability of a Viscous Thread
The linear stability of miscible displacement for radial source flow at infinite P\'eclet number in a Hele-Shaw cell is calculated theoretically. The axisymmetric self-similar flow is shown to be unstable to viscous fingering if the…
A new Rayleigh-type instability is proposed to explain the `sausage-string' pattern of alternating constrictions and dilatations formed in blood vessels under influence of a vasoconstricting agent. Our theory involves the nonlinear…
A classical model of fluid dynamics is considered which describes the shape evolution of a viscous liquid droplet on a homogeneous substrate. All equilibria are characterized and their stability is analyzed by a geometric reduction…
Soft elastic capsules which are driven through a viscous fluid undergo shape deformation coupled to their motion. We introduce an iterative solution scheme which couples hydrodynamic boundary integral methods and elastic shape equations to…
We analyse small-amplitude oscillations of a weakly viscous electrically conducting liquid drop in a strong uniform DC magnetic field. An asymptotic solution is obtained showing that the magnetic field does not affect the shape eigenmodes,…
We consider the dynamics of two layers of incompressible electrically conducting fluid interacting with the magnetic field, which are confined within a 3D horizontally infinite slab and separated by a free internal interface. We assume that…
A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical…
We study the two-dimensional incompressible Navier-Stokes equations in a channel $\Omega=(0,L)\times(0,H)$ with small viscosity $\varepsilon\ll1$, an $\varepsilon$-Navier slip condition on the horizontal walls, and a viscous inflow…
Viscous fingering (VF) is an interfacial instability that occurs in a narrow confinement or porous medium when a less-viscous fluid pushes a more viscous one, producing finger-like patterns. Controlling the VF instability is essential to…
We study the equations obtained from linearizing the compressible Navier-Stokes equations around a steady-state profile with a heavier fluid lying above a lighter fluid along a planar interface, i.e. a Rayleigh-Taylor instability. We…
The breakup of a fluid jet into droplets has long fascinated natural scientists, with early research dating back to the 19th century. Infinitesimal perturbations to a jet grow because of surface tension, which eventually leads to breakup of…
The manuscript focuses on the theoretical stability analysis of the viscous liquid over a vibrating inclined rigid bed when the fluid undergoes an impact of odd viscosity. Such an impact emerges in the classical fluid owing to the broken…
This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a vertically oscillating rigid plane and with an upper boundary given by a free surface. We consider the problem with gravity and surface tension for…
A simple model is proposed for the buckling and coiling instability of a viscous "fluid rope" falling on a plane. By regarding a fluid rope as a one-dimensional flow, this model accounts for only the axial and shared viscous forces. Our…
Vorticity plays a prominent role in the dynamics of incompressible viscous flows. In two-dimensional freely decaying turbulence, after a short transient period, evolution is essentially driven by interactions of viscous vortices, the…
Taylor bubbles are a feature of the slug flow regime in gas-liquid flows in vertical pipes. Their dynamics exhibits a number of transitions such as symmetry-breaking in the bubble shape and wake when rising in downward-flowing and stagnant…
Starch solutions, which are strongly non-Newtonian, show a surface instability, when subjected to a load. A droplet of the fluid is sandwiched between two glass plates and a weight varying from 1 to 5 kgs. is placed on the top plate. The…
Liquid films coating vertical cylinders can form annular liquid collars which translate downwards under gravity. We investigate the dynamics of a thin viscoplastic liquid film coating the interior or exterior of a vertical cylindrical tube,…
Direct numerical simulations of a uniform flow past a fixed spherical droplet are performed to determine the parameter range within which the axisymmetric flow becomes unstable. The problem is governed by three dimensionless parameters: the…
A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied…